In this work, we study the A$_{x}$Fe$_{2-y}$Se$_2$ (A=K, Rb) superconductors using angle-resolved photoemission spectroscopy. In the low temperature state, we observe an orbital-dependent renormalization for the bands near the Fermi level in which the dxy bands are heavily renormliazed compared to the dxz/dyz bands. Upon increasing temperature to above 150K, the system evolves into a state in which the dxy bands have diminished spectral weight while the dxz/dyz bands remain metallic. Combined with theoretical calculations, our observations can be consistently understood as a temperature induced crossover from a metallic state at low temperature to an orbital-selective Mott phase (OSMP) at high temperatures. Furthermore, the fact that the superconducting state of A$_{x}$Fe$_{2-y}$Se$_2$ is near the boundary of such an OSMP constraints the system to have sufficiently strong on-site Coulomb interactions and Hunds coupling, and hence highlight the non-trivial role of electron correlation in this family of iron superconductors.
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